Development of convolutional neural networks for an electron-tracking Compton camera
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Prog. Theor. Exp. Phys. 2021, 083F01 (13 pages)
DOI: 10.1093/ptep/ptab091
Development of convolutional neural networks for
an electron-tracking Compton camera
Tomonori Ikeda1,∗ , Atsushi Takada1 , Mitsuru Abe1 , Kei Yoshikawa1 , Masaya Tsuda1 , Shingo
Ogio1 , Shinya Sonoda1 , Yoshitaka Mizumura2 , Yura Yoshida1 , and Toru Tanimori1
1
Graduate School of Science, Kyoto University, Kitashirakawa Oiwakecho, Sakyo, Kyoto, Kyoto, 606-8502,
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Japan
2
Scientific Balloons, Institute of Space andAstronautical Science, JapanAerospace ExplorationAgency,Yoshin-
odai 3-1-1, Chuou, Sagamihara, Kanagawa, 252-5210, Japan
∗
E-mail: ikeda.tomonori.2s@kyoto-u.ac.jp
Received May 14, 2021; Revised July 2, 2021; Accepted July 5, 2021; Published July 14, 2021
...................................................................................................................
The Electron-Tracking Compton Camera (ETCC), which is a complete Compton camera that
tracks Compton scattering electrons with a gas micro time projection chamber, is expected to
open up MeV gamma-ray astronomy. The technical challenge for achieving several degrees of the
point-spread function is precise determination of the electron recoil direction and the scattering
position from track images. We attempted to reconstruct these parameters using convolutional
neural networks. Two network models were designed to predict the recoil direction and the
scattering position. These models marked 41◦ of angular resolution and 2.1 mm of position
resolution for 75 keV electron simulation data in argon-based gas at 2 atm pressure. In addition,
the point-spread function of the ETCC was improved to 15◦ from 22◦ for experimental data from
a 662 keV gamma-ray source. The performance greatly surpassed that using traditional analysis.
...................................................................................................................
Subject Index F10
1. Introduction
Gamma-ray observations in the low-energy gamma-ray band from a hundred keV to several MeV
address various astrophysical phenomena: nucleosynthesis and the explosion mechanism in super-
novae [1–3], the particle acceleration process in active galactic nuclei or gamma-ray bursts [4–7], and
the electron–positron annihilation line in the Galactic center region [8–10]. However, observation
in this energy band remains poorly explored compared to the X-ray, GeV, and TeV bands, known
as the “MeV gap.” Even now, COMPTEL [11], onboard the Compton Gamma Ray Observatory
launched in 1991, is the most sensitive observer of the MeV sky. The causes of this stagnation in
MeV observation are the huge gamma-ray backgrounds from the atmosphere (albedo) and gener-
ated in the instruments by cosmic-ray interactions. In addition, conventional Compton cameras like
COMPTEL have unclean images according to the Compton circle due to the lack of direction infor-
mation for the recoil electron. Such pseudo imaging is not capable of background rejection and does
not provide quantitative imaging [12]. Thus, it was pointed out that conventional Compton cameras
need the additional parameters of the recoil direction of the Compton electron in order to reduce
backgrounds [13].
The Electron-Tracking Compton Camera (ETCC) is a complete Compton camera that tracks recoil
electrons. It can record all the information on Compton kinematics to overcome the problem of
conventional Compton cameras. Hence, ETCC determines a unique incident gamma-ray direction
[12]. A key device of the ETCC is the tracking detector that detects the recoil electron, since the
© The Author(s) 2021. Published by Oxford University Press on behalf of the Physical Society of Japan.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Funded by SCOAP3PTEP 2021, 083F01 T. Ikeda et al.
point-spread function (PSF) is highly dependent on the determination accuracy of the recoil direction
and the scattering position [14]. Thus, the SMILE group (Sub-MeV gamma-ray Imaging Loaded-on-
ballon Experiment) developed the gas time projection chamber (TPC) based on μ-PIC [15], which
is one of the micro-pattern gas detectors. Although the gas TPC gives us precise track information
for low-energy electrons, these electrons are influenced by multiple scattering and make complex
track images. The technical challenge is the development of the analysis method with an exact
determination of the scattering position and the recoil direction from these track images.
Feature extraction from images is the field of computer vision. Convolutional neural networks
(CNNs) have achieved great success in image classification. Since 2010, many architectures like
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AlexNet [16], VGG [17], GoogLeNet [18], and ResNet [19] were proposed in the ImageNet Large
Scale Visual Recognition Challenge [20] and achieved dramatic progress. In particle physics and
astrophysics experiments, modern machine learning techniques have been actively applied and devel-
oped. They perform several tasks, such as signal–background recognition, particle identification, and
event reconstruction. Machine learning has shown significant performance improvements over the
traditional way based on domain knowledge. In the gas TPC application, a CNN was developed for
polarization extraction from photoelectron track images taken with X-ray polarimeters and improved
the polarization sensitivity by 10%–20% [21]. The NEXT experiment, searching for neutrinoless
double-beta decay, utilized a CNN to identify electron–positron pair production from the topologi-
cal signature; the signal efficiency was improved compared to non-CNN-based analysis [22]. In our
case, a CNN would also be a promising approach.
In this paper we describe the design of CNNs to predict the scattering position and the electron recoil
direction from track images taken by the TPC. In addition, we evaluate the imaging performance for
simulation and experimental data, and compare with a traditional method.
2. The Electron-Tracking Compton Camera
The dominant interaction process of MeV gamma-rays and materials is Compton scattering. A
schematic view of the Compton kinematics is shown in Fig. 1. A conventional Compton camera
obtains the scattering gamma-ray energy Eγ , the absorption position of the scattering gamma-ray
Pabs , the scattering position of the gamma-ray Psct , and the electron recoil energy Ke as well as the
electron recoil direction e. Then, the scattering angle φ is written as
me c2 Ke
cos φ = 1 − . (1)
Eγ + K e Eγ
Conventional Compton cameras are insufficient to resolve the kinematic equation of Compton scat-
tering due to the lack of the electron recoil direction. While the incident gamma direction s is only
reconstructed as a Compton circle, the overlapping of many Compton circles determines the source
location. In a conventional Compton camera, the PSF is only defined by the angular resolution
measure (ARM). The ARM means the angular distance from the reconstructed Compton circle to
the known source location or the determination accuracy of the Compton scattering angle φ. The
ARM depends on the determination accuracies of the absorption point and the scattering point of a
gamma-ray, and the energy resolution.
COMPEL was incredibly successful via Compton imaging techniques. However, the achieved
sensitivity was modest. One of the most important things we learned from COMPTEL is that huge
gamma-ray backgrounds are generated in the satellite itself by cosmic rays. Under such backgrounds,
the sensitivity is overestimated if we only use the ARM. Schönfelder reported the background in
2/13PTEP 2021, 083F01 T. Ikeda et al.
(a) (b)
(c)
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Fig. 1. (a) Schematic view of the ETCC on the SMILE-2+ experiment. The incident gamma-ray coming from
the source location s undergoes Compton scattering into the TPC filled with argon-based gas. The energy,
scattering position Psct , and direction e of the recoil electron are reconstructed by the TPC based on μ-PIC.
Finally, the scattering gamma-ray γ is absorbed at Pabs by pixel scintillator arrays. (b) Schematic image of the
time over threshold. (c) Track images of recoil electrons with 160 keV from μ-PIC anode and cathode strips.
COMPTEL and concluded that the most sensitive way to increase the sensitivity would be to reduce
the instrumental background rate [13]. He also proposed the measurement of recoil electrons in order
to suppress the background. From this effort, we developed ETCC as a next-generation Compton
telescope.
The ETCC provides all the parameters of Compton scattering, including the electron recoil direc-
tion, with the tracking detector. Figure 1(a) shows a schematic view of the ETCC on the SMILE-2+
experiment, which is our second balloon experiment to observe celestial objects at high altitudes
[23]. The ETCC completely resolves the Compton kinematics and determines the unique incident
gamma-ray direction s using the following equation:
Eγ Ke (Ke + 2me c2 )
s = γ + e. (2)
Eγ + K e Eγ + K
The ETCC gives the complete PSF from the ARM and the scattering plane deviation (SPD) [12],
which is the accuracy of the scattering plane determination. The ETCC can achieve high background
rejection power by localizing the arrival direction on the Compton circle thanks to the SPD.
The ETCC of the SMILE-2+ experiment consists of pixel scintillator arrays (PSAs) and a gas
TPC based on a micro pattern gas detector, μ-PIC [15]. The 36 PSAs with a thickness of 26 mm
and the 18 × 4 PSAs with a thickness of 13 mm are arranged below and to the sides of the TPC,
respectively. Each PSA is made of GSO (Gd2 SiO5 :Ce) scintillators of 8 × 8 pixels with a pixel size
of 6 × 6 mm2 . PSAs are deployed as absorbers to detect the energy Eγ and the position Pabs of the
scattering gamma-ray. The TPC is filled with argon-based gas (95% Ar + 3% CF4 + 2% C4 H10 at a
pressure of 2 atm) as a Compton-scattering target and has a drift length of 30 cm. The electron track
and energy information was detected by μ-PIC, which has 768 × 768 strips with a pitch of 400 μm;
the detection volume is 30 × 30 × 30 cm3 . In order to reduce the power consumption, every two
strips of μ-PIC are grouped. Thus, the readout strip pitch is 800 μm in the SMILE-2+ experiment.
3/13PTEP 2021, 083F01 T. Ikeda et al.
The anode and cathode strips of μ-PIC are linearly arranged in the X and Y directions, respec-
tively. The Z direction is reconstructed from the measured drift velocity and drift time. Thus,
two-dimensional images (XZ and YZ) are obtained. The strip signals are processed in FE2009bal
CMOS ASIC chips [24] including preamplifiers, shapers, and comparators. Each amplified signal
is compared to the threshold voltage and synchronized with 100 MHz (10 ns) clocks. Finally, the
addresses of μ-PIC strips with the time-over-threshold (TOT) are recorded. Figure 1(b) shows the
schematic image of the TOT. The TOT is the time between rising and falling edges crossing the
threshold voltage, which is correlated with the convolution of the charge information and the track
length along the Z-axis on each strip. Since the TOT is measured by the comparator at 100 MHz, it
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is digitized at 10 ns. Figure 1(c) shows a typical electron track obtained by μ-PIC. The lengths of
the gray pixels along the Z-axis on each strip correspond to the TOT multiplied by the drift velocity.
The low-density scatter medium and the fine-interval read-out detector of μ-PIC provide fine track
images. The scattering position Psct and electron recoil direction e are reconstructed from these two
images.
The traditional method to determine the scattering position is to utilize the skewness of the TOTs,
which relies on the fact that the stopping power of recoil electrons depends on their residual energy,
and the end-point of the track has large TOTs. The skewness is written by
μ3 (x − x)3
S= = ,
μ2
3/2 (x − x)2 3/2
and is represented as the dimensionless ratio between the third and second moments of the TOTs. The
skewness provides information on whether the endpoint or the start point is on the right or left side
of the image. Consequently, the maximum or minimum of a track image is adopted as a scattering
position. After calculating the scattering position, the recoil direction is determined by a linear fitting
algorithm using TOTs within 4 mm of the reconstructed scattering point to prevent multiple scattering
effects. This method is suitable for relatively straight tracks, while it is less accurate for curved tracks
from multiple scattering.
3. Convolutional neural networks
A CNN is an example of an artificial neural network. It has an input layer, hidden layers, and an output
layer. A hidden layer is generally composed of a combination of a convolutional layer, a pooling
layer, and a fully connected layer. The convolutional layer, which is the most important element in
the CNN, automatically extracts features from the image by a weighting matrix, called a filter or
kernel. The pooling layer is used to down-sample the feature maps extracted in the convolutional
layer by taking an average or maximum. In a fully connected layer, all nodes are connected to all
activations in the previous layer. A deep hierarchical structure of the convolutional and pooling layers
has expressive capacity; a shallow layer learns low-level features or local correlations, and a deep
layer learns high-level features or global correlations. Thus, general CNNs are made up of stacks of
convolutional and pooling layers.
We implemented two independent network models to predict the scattering position and the electron
recoil direction using the Keras/Tensorflow framework [25]. The common point in both network
models is that the input layer takes two-channel images of 256 × 512 pixels, corresponding to
204.8 × 194.56 mm2 , in the XZ and YZ dimensions. Thus, the number of input parameters (φ, cos θ )
is 2 × 256 × 512 (= 262144). In this section we describe the characteristics of these network models.
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Fig. 2. Network model to predict the electron recoil direction. The white and green boxes are the input and
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output layers, respectively. The orange boxes represent convolution layers with stride 1, which are denoted as
(filter size) Conv, (number of filters). The blue boxes are maximum pooling layers with a filter size of 2 × 2
and stride 2. The purple boxes are dropout layers with the rate set to 20%. The pink boxes represent fully
connected or flattening layers.
3.1. Network model to predict the electron recoil direction
In 2014, the Visual Geometry Group (VGG) model [17] received high praise in the classification
category of the image recognition competition. This architecture simply increases the number of
layers by connecting the convolution layer and the fully connected layer. The reduction of the filter
size enables the implementation of a deeper network giving the ability to learn high-level features.
We have designed a network model based on the VGG model to predict the electron recoil direction.
A schematic view of the network model is shown in Fig. 2. This model has two output layers to
predict the cosine of zenith angle cos θ and the azimuth angle φ of the electron recoil direction. The
prediction of each angle is divided into 36 classes, each having a width of 0.055 and 10 degrees,
respectively. Thus, the number of output parameters is 2 × 36. The output layers are activated by
softmax functions to compute each of the probability distributions. The hidden layer is a hierarchical
representation of convolutional and pooling layers. All convolutional layers have a filter size of 3 × 3
and stride 1. All pooling layers take the maximum value with a filter size of 2 × 2 and stride 2.
In addition, three dropout layers, in which some number of layer outputs are randomly ignored,
are deployed to prevent over-fitting. In the final stage, two-dimensional feature maps are converted
to a one-dimensional vector in a flattening layer and connected to the fully connected layer with
512 nodes. All layers except for pooling and output layers are activated by the rectified linear unit
(ReLU) [26].
3.2. Network model to predict the scattering position
The accuracy of the scattering position is expected to be the pixel size resolution. While the VGG
model is able to learn high-level features with the deep layer, the detailed position information is lost at
the same time as the size of the feature maps is reduced. For spatially dense predictions like semantic
segmentation, which is the process of separating an image into some object of interest at a pixel
level, fully convolutional networks (FCNs) [27] and U-Net [28] were developed. These architectures
have an encoder part followed by a decoder part. The encoder part is a typical classifier network like
the VGG. The decoder part expands the feature map and projects onto high-resolution images. In
order to predict the scattering position, we built the network model on the U-Net architecture.
A schematic view of the network model is depicted in Fig. 3. In order to predict the scattering
positions (x, y, z), this model has three output layers, which have linear activation functions. The size
of the output parameter is 3 × 1. The scattering position is predicted on a regression problem. The
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Fig. 3. Network model to predict the scattering position. The white and green boxes are the input and output
layers, respectively. The orange boxes represent convolution layers with stride 1, which are denoted as (filter
size) Conv, (number of filters). The blue boxes are maximum pooling layers with a filter size of 2 × 2 and
stride 2. The purple boxes are dropout layers with the rate set to 20%. The yellow boxes are the unpooling
layers. The pink box represents a flatten layer. The black dotted arrows indicate the concatenation operation
to combine the output of the convolution layers in the encoder part with the decoder part.
hidden layer is comprised of the encoder and decoder part. The first encoder section extracts features
at different scale sizes with down-sampling as well as the network to predict the electron recoil
direction. The convolutional layers have 3 × 3 kernels with stride 1, and the pooling layers are the
maxpooling operation and stride 2. In the second decoder section, the pooling layers are replaced with
unpooling layers for up-sampling and expanding feature maps. We deploy the convolution transpose
layer as an unpooling operation with a filter size of 2 × 2 and stride 2. In addition, up-sampling
images are connected by down-sampling images in concatenation layers and recover the high spatial
resolution. The final up-sampling layer is flattened and connected to the output layers. All the layers
except for the pooling and output layers are activated by the ReLU.
4. Training and validating the network via a Monte Carlo simulation
4.1. Preparing a training and validation data set
The training and validation data are prepared by the Monte Carlo (MC) simulation package of the
SMILE experiment based on Geant4 [29]. In order to gernerate experimental images, the following
procedures are undertaken:
◦ The full detector geometry is constructed in Geant4. Electron beams are generated in the TPC
volume with uniform position and direction. Then, the interaction points and the deposit energies
are recorded.
◦ From the deposit energies, the number of ionized electrons is calculated considering the Fano
factor. In addition, the collected positions of ionized electrons on μ-PIC strips are obtained
according to the diffusion effect simulated by MAGBOLTZ [30].
◦ Waveforms of μ-PIC strips are represented by overlapping waveform templates, which are
calculated from the simulated μ-PIC pulse signal using Garfiled++ [31]. These waveforms are
digitized and TOTs are obtained by comparing to the threshold. Finally, the calculated TOTs
are encoded to the experimental data format.
We analyze simulated data and make XZ and YZ images of 256 × 512 pixels so that the tracks are
in the center of the images, like Fig. 1(c). Overall, 630k and 70k MC events for 5–200 keV, which
6/13PTEP 2021, 083F01 T. Ikeda et al.
were fully contained in the TPC volume, were generated for the training and validation data sets,
respectively. Also, each class has almost the same number of samples; one class has about 17500
samples for the training data set.
4.2. Training and validation network
We trained the networks and optimized the learnable parameters by minimizing the loss function
between the ground truth and the prediction. In training the model to predict the electron recoil
direction, the ground truth is expressed by a “one-hot” vector p. For example, the ith class constitutes
angles φ ranging from πi/18 − π to π(i + 1)/18 − π. Then, the ith label is 1 and the rest 0 in the one-
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hot vector. We employed the cross-entropy loss, which is a typical loss function in the classification
task, represented by H (p, q) = −i pi log qi , where pi is the ith label of the ground truth and qi is the
predicted one. On the other hand, we employed the mean square root as a loss function to train the
model to predict the scattering position. In both cases, an Adam optimizer was used to minimize the
loss function with a learning rate of 0.0001. A batch size of four was chosen. We trained the models
for ten epochs where validation losses saturated. The huge amount of calculations wer performed on
NVIDIA Geforce GTX 2070 super graphics processing units (GPUs).
Figure 4 shows confusion matrices at the φ and cos θ class predictions of several energies. In 5–
10 keV of φ, the CNN almost misclassifies and outputs two indexes in any true φ. We confirmed that
such a high bias prediction appears when the highest predicted probability is very low. Therefore,
the angle φ is determined by random uniformly in such a case. As the highest predicted probability
exceeds a certain threshold, the predicted angle φ is calculated as follows:
N −1
c c −1
N
φ = atan2 pi sin φi , pi cos φi , (3)
i=0 i=0
where pi is the predicted probability in the ith class, φi is the center angle of the ith class, and Nc is
the number of classes. The correlation matrix between the calculated angle φ and the true angle φ
are shown in Fig. 5. The high bias prediction in 5–10 keV was reduced due to the uniform random.
On the other hand, some bias prediction or nonuniform angular response remains in 10–200 keV. In
order to remove the nonuniform response, adding the nonuniform penalty term to the loss function
is valuable as discussed in Ref. [21]. We will deploy such an advanced method in our future work.
The angle θ is calculated the same way. The confusion matrices and correlation matrices of cos θ
are described in the bottom panels of Figs. 4 and 5, respectively.
Two values are evaluated. The first is the angular error, cos θerr = Vt ·Vp , where Vt and Vp are the true
and predicted recoil vectors, respectively. The second value is the position error, Rerr = |P t − P p |,
where Pt and Pp are the true and predicted scattering positions, respectively. We obtained these
distributions for 70k validation data values. The angular and position resolutions are defined by the
50% area values. In the traditional method, these values are calculated in the same way.
Several reconstructed examples are depicted in Fig. 6. Using the traditional method, high-energy
recoil events like the bottom figures could not be reconstructed with high precision due to the multiple
scattering effect. On the other hand, the CNN succeeded in resolving the scattering point and recoil
direction for such events.
Figures 7(a) and (b) show the energy dependence of the angular resolution and the position res-
olution compared to the traditional method. The CNN method is better than the traditional method
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Fig. 4. Confusion matrices at the φ (top panel) and cos θ (bottom panel) class predictions.
Fig. 5. Top: The correlation matrices between the calculated angle φ and the true angle φ. Bottom: The
correlation matrices between the calculated cos θ and the true cos θ.
Fig. 6. Four track images with the predicted scattering positions and recoil directions. The red points and
arrows are the true scattering points and recoil directions, while the blue squares and arrows are the predictions
using the CNN.
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(a) (b)
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Fig. 7. (a) Angular resolution of the CNN method compared to the traditional method using the simulation
data. The red and blue points indicate the CNN and traditional methods, respectively. The black dashed line
is the principle limit of multiple scatterings with a 0.8 mm pitch readout. (b) Position resolution of the CNN
method compared to the traditional method. The red and blue points are the CNN and traditional methods,
respectively.
above 20 keV. In particular, it achieved excellent performance above 50 keV. The angular resolu-
tion for 75 keV is 41◦ . For predicting the scattering position, the CNN method indicates better
performance at all energies. The position resolution at 75 keV is 2.1 mm.
5. Performance of ETCC using the CNN method
We conducted the ETCC calibration measurement for the SMILE-2+ instrument on the ground. In
order to investigate several energy responses, calibration data for 133 Ba (mainly 356 keV), 22 Na
(511 keV), 137 Cs (662 keV), and 60 Co (1173 keV and 1332 keV) were taken. In addition, the 137 Cs
source was placed at several zenith positions separated by 183 cm from the ETCC center. We reana-
lyzed these calibration data with the CNN method and evaluated the performance of the experimental
ETCC data.
5.1. Event selection
The calibration measurements involve not only direct incident gamma-rays from the source but also
backgrounds of ambient gamma-rays and cosmic rays. Therefore, we adopted the following event
selection to extract direct incident gamma-rays from the sources.
◦ One hit event: We require one track in the TPC and one hit pixel signal in the PSA, which
removed most accidental coincidence events.
◦ Fiducial volume: We require that an electron track is contained within the fiducial volume of
25.72 × 25.72 × 29.8 cm3 . At the boundary of the detection area, the electric field is distorted
due to the supply voltage of the PMT of the PSA around the TPC. Such events which do not
retain the original track information are eliminated.
◦ Fully contained electron: The dE/dx distribution or the correlation between the track length and
the energy deposit of the track in the TPC distinguishes the fully contained electrons, escaped
electrons from the TPC, and cosmic-ray muons. The dE/dx of a fully contained electron is
empirically proportional to E 1.72 [32] of the recoil electron energy. We determined the fully
contained electron band by fitting with a Gaussian function every energy bin with a width of
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(a) (b) (c)
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Fig. 8. (a) ARM, (b) SPD, and (c) cos θ distributions of the experiment data. The red and blue histograms,
which are normalized by the total areas, indicate the CNN and traditional methods, respectively.
10 keV, and the region within the ±3 σ quantiles was chosen. More details can be found in
Ref [14].
◦ Compton kinematic test: The angle between the recoil electron direction and the scattering
gamma direction is defined as the Compton α angle and calculated geometrically by
cos αgeo = g · e. (4)
In addition, this angle is derived by the Compton scattering kinematics:
me c2 Ke
cos αkin = 1 − . (5)
Eγ Ke + 2me c2
Therefore, cos α (= cos αgeo − cos αkin ) being nearly zero ensures that the reconstructed
events are true Compton scattering events. We applied the limit | cos α| < 0.5 in order to
extract Compton scattering events.
◦ Energy selection: Events with a reconstructed energy within twice the full width at half
maximum (FWHM) for the source energy are used to extract the direct components.
After the event selection, the effective areas of the experimental and simulation data for 662 keV
were 2.3 × 10−1 cm2 and 2.1 × 10−1 cm2 , respectively.
5.2. Imaging performance
The incident gamma-ray direction is reconstructed by Eq. (2). To evaluate the reconstruction accuracy,
we defined the error angle cos θ between the reconstructed vector and the source vector. The PSF is
the angular resolution of θ. Thus, we calculated the value of half the area of the cos θ distribution
as the PSF. Figure 8 shows the ARM, SPD, and cos θ distribution using the CNN and traditional
methods with the 137 Cs calibration source at the zenith = 0. The ARM using the CNN method is 10◦
and is not different from the traditional method. We confirmed that the supply voltage of the PSAs
around TPC distorted the electric field, and this dominated the uncertainty of the scattering position.
On the other hand, the SPD was highly improved thanks to reducing the angular resolution of the
recoil direction. We obtained 59◦ (FWHM) for the SPD by fitting a Gaussian function. This benefit
gave a sharp cos θ distribution and improved the PSF to 15◦ .
Figures 9(a) and (b) show the dependencies of the PSF on the gamma-ray energy and the incident
zenith angle, respectively. For every gamma-ray energy and incident zenith angle, the CNN method
performed markedly better than the traditional method.
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(a) (b)
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Fig. 9. (a) Gamma-ray energy dependence and (b) incident zenith angle dependence of PSF. The red and blue
lines indicate the experimental data using the CNN method and traditional methods, respectively. The gray
dots and triangles are the simulation data using the CNN and traditional methods, respectively.
Fig. 10. Reconstructed source images of 137 Cs set at zenith angles of 0, 30, 60, and 90◦ for the experimental
data. The top and bottom columns are the CNN and traditional methods, respectively.
Reconstructed source images for 137 Cs at several zenith angles are shown in Fig. 10 using an
equal-solid-angle projection, such as the Lambert projection. The bright points representing sources
were observed, and the more focused images were confirmed in the CNN method.
6. Discussion
Since the scattering position resolution is smaller than the PSA position uncertainty, further improve-
ment in the scattering points cannot be expected to improve the PSF. On the other hand, the SPD has
potential for improvement. Although the recoil direction was dramatically improved using CNN, the
physical limit of the multiple scattering has not yet been reached. As the angular resolutions of the
azimuth and the zenith angles were calculated separately for 50 keV electrons at a 4 mm distance
from the scattering points, 29◦ and 35◦ were obtained, respectively. This indicates that the zenith
angular resolution mainly determines the 3D angular resolution. The Z-direction position resolution
has a width corresponding to the TOT. From a rough calculation, a drift speed of 38 mm μs−1 and
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TOT width of 80 ns corresponding to a 0.5 pC input charge give a 3.0 mm position resolution, which
is 3.8 times worse than the 800 μm read-out pitch of the X and Y directions. This is the cause of
smearing of the track information for low-energy electrons, as can be seen from the 42.3 keV image
in the upper left of Fig. 6. Improvement can be expected by using a short shaping time amplifier.
Also, waveforms taken by the flush ADC have Z-direction information [33]. Therefore, utilizing
the waveform images in CNNs would be a good approach. Regarding the azimuth direction, it is
adequate to make the read-out pitch more acceptable and increase the track information using, for
example, a three-projection read-out system [34,35]. We confirmed that a three-projection read-out
system with 480 μm pitch achieved 50◦ of 3D angular resolution from the simulation.
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In this research, a network based on the VGG model was used as a demonstration. However,
residual networks [19] (ResNet) have mainly been used to realize deeper layers in recent research.
In the future, we will incorporate this technology to improve the neural network aspect.
7. Conclusion
We designed two CNNs based on the VGG and U-Net models to predict the scattering position and the
electron recoil direction from track images taken by the ETCC. The angular resolution and scattering
position resolution utilizing CNNs were obtained as 41◦ and 2.1 mm for 75 keV simulation data. As
we adopted the CNN analysis for experimental calibration data, the resulting PSF was improved
by 32% compared with the traditional analysis and achieved 15◦ . The CNN analysis surpassed the
traditional analysis, and the improved ETCC has the potential to reveal the MeV gamma-ray sky.
Acknowledgements
This work was partly supported by Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant-in-
Aids for Scientific Research) (grant no. 20K20428).
Funding
Open Access funding: SCOAP3 .
References
[1] S. M. Matz, G. H. Share, M. D. Leising, E. L. Chupp, W. T. Vestrandt, W. R. Purcell, M. S. Strickman,
and C. Reppin, Nature 331, 416 (1988).
[2] R. Diehl, et al., Astron. Astrophys. 411, L451 (2003).
[3] E. Churazov et al., Astrophys. J. 812, 62 (2015).
[4] M. Chiaberge, A. Capetti, and A. Celotti, Mon. Not. Roy. Astron. Soc. 324, L33 (2001).
[5] L. Ballo et al., Astrophys. J. 567, 50 (2002).
[6] M. S. Briggs et al., Astrophys. J. 524, 82 (1999).
[7] R. D. Preece, M. S. Briggs, R. S. Mallozzi, G. N. Pendleton, W. S. Paciesas, and D. L. Ban, Astrophys.
J. Suppl. Ser. 126, 19 (2000).
[8] W. R. Purcell, L.-X. Cheng, D. D. Dixon, R. L. Kinzer, J. D. Kurfess, M. Leventhal, M. A. Saunders,
J. G. Skibo, D. M. Smith, and J. Tueller, Astrophys. J. 491, 725 (1997).
[9] T. Siegert, R. Diehl, G. Khachatryan, M. G. H. Krause, F. Guglielmetti, J. Greiner, A. W. Strong, and
X. Zhang, Astron. Astrophys. 586, A84 (2016).
[10] C. A. Kierans et al., Astrophys. J. 895, 44 (2020).
[11] V. Schönfelder et al., Astron. Astrophys. Supp. Ser. 143, 145 (2000).
[12] T. Tanimori et al., Sci. Rep. 7, 41511 (2017).
[13] V. Schönfelder, New Astron. Rev. 48, 193 (2004).
[14] T. Tanimori et al., Astrophys. J. 810, 28 (2015).
[15] A. Takada et al., Nucl. Instr. Meth. Phys. Res. A 573, 195 (2007).
12/13PTEP 2021, 083F01 T. Ikeda et al.
[16] A. Krizhevsky, I. Sutskever, and G.E. Hinton, in Proc. 25th Int. Conf. Neural Information Processing
Syst., eds. F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger (2012), Vol. 1.
[17] K. Simonyan and A. Zisserman, arXiv:1409.1556 [cs.CV] [Search INSPIRE].
[18] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and
A. Rabinovich, arXiv:1409.4842 [cs.CV] [Search INSPIRE].
[19] K. He, X. Zhang, S. Ren, and J. Sun, in Proc. IEEE Conf. Computer Vision and Pattern Recognition
(CVPR) (IEEE, New York, 2016), p. 770.
[20] O. Russakovsky et al., arXiv:1409.0575 [cs.CV] [Search INSPIRE].
[21] T. Kitaguchi, K. Black, T. Enoto, A. Hayato, J. E. Hill, W. B. Iwakiri, P. Kaaret, T. Mizuno, and
T. Tamagawa, Nucl. Instr. Meth. Phys. Res. A 942, 162389 (2019).
[22] M. Kekic et al. [NEXT collaboration], J. High Energy Phys. 2101, 189 (2021).
Downloaded from https://academic.oup.com/ptep/article/2021/8/083F01/6321246 by guest on 27 September 2021
[23] T. Tanimori [on behalf of SMILE project], J. Phys.: Conf. Ser. 1468, 012046 (2020).
[24] T. Mizumoto et al., Nucl. Instr. Meth. Phys. Res. A 800, 40 (2015).
[25] M. Abadi et al. arXiv:1603.04467 [cs.DC] [Search INSPIRE].
[26] V. Nair and G. E. Hinton, in Proc. 27th Int. Conf. Int. Conf. Machine Learning, eds. J. Fürnkranz and
T. Joachims. (Omnipress, Madison, WI, 2010), p. 807.
[27] E. Shelhamer, J. Long, and T. Darrell, IEEE Trans. Patt. Anal. Mach. Intel. 39, 640 (2017).
[28] O. Ronneberger, P. Fischer, and T. Brox, in Proc. 18th Int. Conf. Medical Image Computing and
Computer-Assisted Intervention (MICCAI), eds. N. Navab, J. Hornegger, W. M. Wells, and A. F. Frangi
(Springer, New York, 2015), Vol. 3, p. 234.
[29] S. Agostinelli et al., Nucl. Instr. Meth. Phys. Res. A 506, 250 (2003).
[30] S. F. Biagi, Nucl. Instr. Meth. Phys. Res. A 283, 716 (1989).
[31] A. Takada et al., J. Instrum. 8, C10023 (2013).
[32] F. Sauli, CERN-77-09 (CERN, Geneva, 2004).
[33] J. B. R. Battat et al., J. Instrum. 11, P10019 (2016).
[34] F. Sauli, T. Meinschad, L. Musa, and L. Ropelewski, Conf. Rec. IEEE Symp. Nucl. Sci., (IEEE, New
York, 2004), Vol. 1, p. 12.
[35] M. Diwan, M. Potekhin, V. Viren, X. Qian, and C. Zhang, J. Phys. Conf. Ser. 762, 012033 (2016).
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